HW2
AhmetCosgun
October 25, 2018
Task 1 a
Read data from rds files, get unique instances, include selected bet types=“1x2”,“bts”,“ha”,“ou”,“dc”, only work with initial odd
matchdata<-readRDS('C:\\Users\\10025\\Desktop\\IE582\\hw2/df9b1196-e3cf-4cc7-9159-f236fe738215_matches.rds', refhook = NULL)
odddata<-data.table(readRDS('C:\\Users\\10025\\Desktop\\IE582\\hw2/df9b1196-e3cf-4cc7-9159-f236fe738215_odd_details.rds', refhook = NULL))
matchdata=matchdata[complete.cases(matchdata)]
matchdata<-unique(matchdata)
odddata<- odddata[betType %in% c("1x2","bts","ha","ou","dc")]
odddata=odddata[order(matchId, oddtype,bookmaker,date)]
odddata_initial=odddata[,list(start_odd=odd[1]),
by=list(matchId,oddtype,bookmaker,totalhandicap)]Select 5 bookmakers, and combined them into one dataset
odddata_initial_10Bet<-odddata_initial[bookmaker=="10Bet"]
wide_odds_initial_10Bet=dcast(odddata_initial_10Bet,
matchId~oddtype+totalhandicap,
value.var='start_odd')
odddata_initial_bet365<-odddata_initial[bookmaker=="bet365"]
wide_odds_initial_bet365=dcast(odddata_initial_bet365,
matchId~oddtype+totalhandicap,
value.var='start_odd')
odddata_initial_BetfairExchange<-odddata_initial[bookmaker=="Betfair Exchange"]
wide_odds_initial_BetfairExchange=dcast(odddata_initial_BetfairExchange,
matchId~oddtype+totalhandicap,
value.var='start_odd')
odddata_initial_bwin<-odddata_initial[bookmaker=="bwin"]
wide_odds_initial_bwin=dcast(odddata_initial_bwin,
matchId~oddtype+totalhandicap,
value.var='start_odd')
odddata_initial_Betsson<-odddata_initial[bookmaker=="Betsson"]
wide_odds_initial_Betsson=dcast(odddata_initial_Betsson,
matchId~oddtype+totalhandicap,
value.var='start_odd')
m <- rbind(wide_odds_initial_10Bet, wide_odds_initial_bet365,wide_odds_initial_BetfairExchange,wide_odds_initial_bwin,wide_odds_initial_Betsson, fill=TRUE)For combined dataset
z<-merge(x = matchdata, y = m, by = "matchId", all = TRUE,allow.cartesian=TRUE)
z<-setDT(z)[, paste0("score", 1:2) := tstrsplit(score, ":")]
z[,72]<-as.numeric(unlist(z[,72]))
z[,73]<-as.numeric(unlist(z[,73]))
z$totalscore<-z$score1+z$score2
z$ou<-ifelse(z[,74]<2.5,"1","2")
z[,75]<-as.numeric(unlist(z[,75]))
data<-z[,-c(1:7)]
data_ou25<-data[!(is.na(data$over_2.5) | data$over_2.5==""), ]
asdas<-data_ou25[,c("over_0.5","over_0.75", "over_1", "over_1.75", "over_10", "over_10.5", "over_11", "over_11.5", "over_2", "over_2.25", "over_2.29", "over_2.75", "over_3", "over_3.25", "over_3.75", "over_4", "over_4.25", "over_4.5", "over_5","over_5.25","over_5.5","over_6.5","over_7.5", "over_8.5"):=NULL]
asdas<-asdas[,c("under_0.5","under_0.75", "under_1", "under_1.75", "under_10", "under_10.5", "under_11", "under_11.5", "under_2", "under_2.25", "under_2.29", "under_2.75", "under_3", "under_3.25", "under_3.75", "under_4", "under_4.25", "under_4.5", "under_5","under_5.25","under_5.5","under_6.5","under_7.5", "under_8.5"):=NULL]
pat=asdas[complete.cases(asdas)]
dat<-pat[,-c(17:20)]
ress<-pat[,c(20)]
a<-as.numeric(unlist(ress[,1]))
pc <- princomp(dat)
plot(pc)
summary(pc, loadings=T)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 4.5147411 2.1823122 1.41829685 0.8848934 0.75133113
## Proportion of Variance 0.7046297 0.1646376 0.06953917 0.0270693 0.01951452
## Cumulative Proportion 0.7046297 0.8692672 0.93880640 0.9658757 0.98539023
## Comp.6 Comp.7 Comp.8 Comp.9
## Standard deviation 0.493618466 0.261880530 0.193129893 0.182370733
## Proportion of Variance 0.008423217 0.002370837 0.001289419 0.001149756
## Cumulative Proportion 0.993813450 0.996184287 0.997473706 0.998623462
## Comp.10 Comp.11 Comp.12 Comp.13
## Standard deviation 0.1151012584 0.1067004306 0.0784575025 0.0748793518
## Proportion of Variance 0.0004579893 0.0003935751 0.0002127964 0.0001938293
## Cumulative Proportion 0.9990814509 0.9994750260 0.9996878223 0.9998816516
## Comp.14 Comp.15 Comp.16
## Standard deviation 4.433805e-02 3.203779e-02 2.076518e-02
## Proportion of Variance 6.795922e-05 3.548301e-05 1.490619e-05
## Cumulative Proportion 9.999496e-01 9.999851e-01 1.000000e+00
##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
## 1_NA 0.157 0.410 0.319 0.264 0.198 0.672 0.189
## 12_NA
## 1X_NA 0.164 0.113 0.212
## 2_NA -0.557 -0.123 0.651 -0.422 0.130 0.221
## NO_NA -0.212 0.764 -0.254
## X2_NA -0.204 0.136 0.264 -0.412 -0.791
## YES_NA -0.136 0.125 0.111 0.383 -0.444
## odd1_NA 0.197 0.662 0.239 -0.156 0.204 -0.456 -0.413 -0.115
## odd2_NA -0.723 0.215 -0.351 0.393 0.218 -0.314
## oddX_NA -0.198 0.414 -0.168 -0.336 0.769 0.132 0.184
## over_1.5
## over_2.5 -0.164 -0.236 0.135 0.104
## over_3.5 -0.425 -0.642 0.379 0.287 -0.132
## under_1.5 -0.119 0.329 -0.113 -0.232 -0.751 0.249 -0.157 -0.199
## under_2.5 0.114 -0.251
## under_3.5 -0.109
## Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16
## 1_NA 0.185 0.251
## 12_NA 0.171 -0.337 0.914
## 1X_NA -0.580 -0.692 -0.272
## 2_NA
## NO_NA 0.286 0.417 -0.118
## X2_NA 0.121 0.207
## YES_NA -0.504 -0.566 -0.116 0.104
## odd1_NA
## odd2_NA
## oddX_NA
## over_1.5 0.273 -0.952
## over_2.5 0.287 -0.326 -0.585 0.551 -0.162 0.140
## over_3.5 0.226 0.236 -0.197
## under_1.5 -0.310
## under_2.5 0.665 -0.515 0.287 -0.244 0.157 -0.183
## under_3.5 0.119 0.142 -0.121 0.931 0.252# Get principal component vectors using prcomp instead of princomp
pc = prcomp(dat,center = TRUE,scale = TRUE)
# First 7 principal components
comp <- data.frame(pc$x[,1:7])
# Plot
plot(comp, pch=16, col=a, main="Graph of Different PCs in 2-D")
ind <- get_pca_ind(pc)
f<-ind$coord
##eigenvalues
eig.val <- get_eigenvalue(pc)
eig.val## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 5.81520173 36.34501083 36.34501
## Dim.2 4.26233605 26.63960033 62.98461
## Dim.3 3.38070808 21.12942550 84.11404
## Dim.4 1.21447177 7.59044858 91.70449
## Dim.5 0.37108323 2.31927021 94.02376
## Dim.6 0.32281186 2.01757413 96.04133
## Dim.7 0.22805859 1.42536620 97.46670
## Dim.8 0.13588317 0.84926984 98.31597
## Dim.9 0.07785377 0.48658606 98.80255
## Dim.10 0.05470026 0.34187664 99.14443
## Dim.11 0.03795848 0.23724050 99.38167
## Dim.12 0.02725929 0.17037057 99.55204
## Dim.13 0.02272841 0.14205258 99.69409
## Dim.14 0.02086661 0.13041631 99.82451
## Dim.15 0.01632796 0.10204978 99.92656
## Dim.16 0.01175071 0.07344194 100.00000fviz_eig(pc)
##graph of indiviudals
fviz_pca_ind(pc,
#col.ind = "cos2", # Color by the quality of representation
col.ind = a, # Color by the quality of representation
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07")
)
##graph of variables
fviz_pca_var(pc,
col.var = "contrib", # Color by contributions to the PC
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
)
##graph combined
fviz_pca_biplot(pc, #repel = TRUE,
col.var = "#2E9FDF", # Variables color
col.ind = a
)
For only 1 bookmaker
z1<-merge(x = matchdata, y = wide_odds_initial_10Bet, by = "matchId", all = TRUE,allow.cartesian=TRUE)
z1<-setDT(z1)[, paste0("score", 1:2) := tstrsplit(score, ":")]
z1[,70]<-as.numeric(unlist(z1[,70]))
z1[,71]<-as.numeric(unlist(z1[,71]))
z1$totalscore<-z1$score1+z1$score2
z1$ou<-ifelse(z1[,72]<2.5,"1","2")
z1[,73]<-as.numeric(unlist(z1[,73]))
data1<-z1[,-c(1:7)]
data1_ou25<-data1[!(is.na(data1$over_2.5) | data1$over_2.5==""), ]
asdas1<-data1_ou25[,c("over_0.5","over_0.75", "over_1", "over_1.75", "over_10", "over_10.5", "over_11", "over_11.5", "over_2", "over_2.25", "over_2.29", "over_2.75", "over_3", "over_3.25", "over_3.75", "over_4", "over_4.25", "over_4.5", "over_5","over_5.25","over_5.5","over_6.5","over_7.5"):=NULL]
asdas1<-asdas1[,c("under_0.5","under_0.75", "under_1", "under_1.75", "under_10", "under_10.5", "under_11", "under_11.5", "under_2", "under_2.25", "under_2.29", "under_2.75", "under_3", "under_3.25", "under_3.75", "under_4", "under_4.25", "under_4.5", "under_5","under_5.25","under_5.5","under_6.5","under_7.5"):=NULL]
pat1=asdas1[complete.cases(asdas1)]
dat1<-pat1[,-c(17:20)]
ress1<-pat1[,c(20)]
a1<-as.numeric(unlist(ress1[,1]))
pc1 <- princomp(dat1)
plot(pc1)
summary(pc1, loadings=T)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 5.100364 2.2335837 0.79667758 0.415445890
## Proportion of Variance 0.813601 0.1560320 0.01985064 0.005398066
## Cumulative Proportion 0.813601 0.9696331 0.98948369 0.994881756
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 0.253697098 0.207286900 0.1771706641 0.1028758624
## Proportion of Variance 0.002012984 0.001343857 0.0009817318 0.0003310063
## Cumulative Proportion 0.996894740 0.998238596 0.9992203280 0.9995513343
## Comp.9 Comp.10 Comp.11 Comp.12
## Standard deviation 0.081885891 0.063207507 4.316411e-02 2.679655e-02
## Proportion of Variance 0.000209714 0.000124953 5.827132e-05 2.245778e-05
## Cumulative Proportion 0.999761048 0.999886001 9.999443e-01 9.999667e-01
## Comp.13 Comp.14 Comp.15 Comp.16
## Standard deviation 2.310965e-02 1.994775e-02 9.955158e-03 5.716233e-03
## Proportion of Variance 1.670306e-05 1.244506e-05 3.099599e-06 1.021949e-06
## Cumulative Proportion 9.999834e-01 9.999959e-01 9.999990e-01 1.000000e+00
##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
## 1_NA 0.149 0.453 0.130 0.787 0.225
## 12_NA 0.160
## 1X_NA 0.196 0.133 -0.111 0.343
## 2_NA -0.473 -0.819 -0.171 -0.235
## NO_NA -0.181 -0.114 -0.178 0.643
## X2_NA -0.194 -0.181 0.149 0.898 0.295
## YES_NA 0.178 0.170 -0.527
## odd1_NA 0.243 0.722 0.270 -0.279 -0.495 -0.103
## odd2_NA -0.782 0.154 0.198 0.534 -0.194
## oddX_NA -0.172 0.313 0.870 -0.112 -0.215 -0.214
## over_1.5
## over_2.5 0.223 0.200
## over_3.5 -0.194 0.579 0.222 -0.195 0.631
## under_1.5 0.225 -0.588 -0.152 0.602 -0.245
## under_2.5 -0.223 0.225
## under_3.5 -0.101 0.125
## Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16
## 1_NA 0.258
## 12_NA 0.183 0.366 0.793 0.389 -0.142
## 1X_NA -0.846 -0.284
## 2_NA
## NO_NA 0.650 -0.227
## X2_NA
## YES_NA -0.439 0.659
## odd1_NA
## odd2_NA
## oddX_NA
## over_1.5 0.495 -0.856
## over_2.5 0.307 0.251 -0.856
## over_3.5 -0.142 -0.152 0.265
## under_1.5 -0.311 0.183
## under_2.5 -0.116 0.778 -0.432 0.140 -0.206 -0.117
## under_3.5 0.197 0.821 0.490# Get principal component vectors using prcomp instead of princomp
pc1 = prcomp(dat1,center = TRUE,scale = TRUE)
# First 7 principal components
comp1 <- data.frame(pc1$x[,1:7])
# Plot
plot(comp1, pch=16, col=a1, main="Graph of Different PCs in 2-D")
ind1 <- get_pca_ind(pc1)
f1<-ind1$coord
##eigenvalues
eig.val1 <- get_eigenvalue(pc1)
eig.val1## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 8.428183983 52.676149892 52.67615
## Dim.2 4.836710913 30.229443204 82.90559
## Dim.3 2.197274492 13.732965577 96.63856
## Dim.4 0.215728471 1.348302944 97.98686
## Dim.5 0.107191178 0.669944864 98.65681
## Dim.6 0.068191267 0.426195417 99.08300
## Dim.7 0.048488311 0.303051943 99.38605
## Dim.8 0.032060096 0.200375602 99.58643
## Dim.9 0.019873122 0.124207013 99.71064
## Dim.10 0.015732548 0.098328428 99.80896
## Dim.11 0.008413168 0.052582299 99.86155
## Dim.12 0.007891985 0.049324905 99.91087
## Dim.13 0.005736325 0.035852032 99.94672
## Dim.14 0.003787905 0.023674405 99.97040
## Dim.15 0.003139243 0.019620267 99.99002
## Dim.16 0.001596993 0.009981207 100.00000fviz_eig(pc1)
##graph of indiviudals
fviz_pca_ind(pc1,
#col.ind = "cos2", # Color by the quality of representation
col.ind = a1, # Color by the quality of representation
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07")
#repel = TRUE # Avoid text overlapping
)
##graph of variables
fviz_pca_var(pc1,
col.var = "contrib", # Color by contributions to the PC
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
)
##graph combined
fviz_pca_biplot(pc1, #repel = TRUE,
col.var = "#2E9FDF", # Variables color
col.ind = a1
# col.ind = "#696969" # Individuals color
)
##Task 2
z$totalscore<-z$score1+z$score2
z$ou<-ifelse(z$score1==z$score2,"1",ifelse(z$score1>z$score2,"2","3"))
z1x2<-z
z1x2[,75]<-as.numeric(unlist(z1x2[,75]))
data1x2<-z1x2[,-c(1:7)]
data_1x2<-data1x2[!(is.na(data$odd1_NA) | data$odd1_NA==""), ]
asdas1x2<-data_1x2[,c("over_0.5","over_0.75", "over_1", "over_1.75", "over_10", "over_10.5", "over_11", "over_11.5", "over_2", "over_2.25", "over_2.29", "over_2.75", "over_3", "over_3.25", "over_3.75", "over_4", "over_4.25", "over_4.5", "over_5","over_5.25","over_5.5","over_6.5","over_7.5", "over_8.5"):=NULL]
asdas1x2<-asdas1x2[,c("under_0.5","under_0.75", "under_1", "under_1.75", "under_10", "under_10.5", "under_11", "under_11.5", "under_2", "under_2.25", "under_2.29", "under_2.75", "under_3", "under_3.25", "under_3.75", "under_4", "under_4.25", "under_4.5", "under_5","under_5.25","under_5.5","under_6.5","under_7.5", "under_8.5"):=NULL]
pat1x2=asdas1x2[complete.cases(asdas1x2)]
dat1x2<-pat1x2[,-c(17:20)]
ress1x2<-pat1x2[,c(20)]
a1x2<-as.numeric(unlist(ress1x2[,1]))
pc1x2 <- princomp(dat1x2)
plot(pc1x2)
summary(pc1x2, loadings=T)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 4.5147411 2.1823122 1.41829685 0.8848934 0.75133113
## Proportion of Variance 0.7046297 0.1646376 0.06953917 0.0270693 0.01951452
## Cumulative Proportion 0.7046297 0.8692672 0.93880640 0.9658757 0.98539023
## Comp.6 Comp.7 Comp.8 Comp.9
## Standard deviation 0.493618466 0.261880530 0.193129893 0.182370733
## Proportion of Variance 0.008423217 0.002370837 0.001289419 0.001149756
## Cumulative Proportion 0.993813450 0.996184287 0.997473706 0.998623462
## Comp.10 Comp.11 Comp.12 Comp.13
## Standard deviation 0.1151012584 0.1067004306 0.0784575025 0.0748793518
## Proportion of Variance 0.0004579893 0.0003935751 0.0002127964 0.0001938293
## Cumulative Proportion 0.9990814509 0.9994750260 0.9996878223 0.9998816516
## Comp.14 Comp.15 Comp.16
## Standard deviation 4.433805e-02 3.203779e-02 2.076518e-02
## Proportion of Variance 6.795922e-05 3.548301e-05 1.490619e-05
## Cumulative Proportion 9.999496e-01 9.999851e-01 1.000000e+00
##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
## 1_NA 0.157 0.410 0.319 0.264 0.198 0.672 0.189
## 12_NA
## 1X_NA 0.164 0.113 0.212
## 2_NA -0.557 -0.123 0.651 -0.422 0.130 0.221
## NO_NA -0.212 0.764 -0.254
## X2_NA -0.204 0.136 0.264 -0.412 -0.791
## YES_NA -0.136 0.125 0.111 0.383 -0.444
## odd1_NA 0.197 0.662 0.239 -0.156 0.204 -0.456 -0.413 -0.115
## odd2_NA -0.723 0.215 -0.351 0.393 0.218 -0.314
## oddX_NA -0.198 0.414 -0.168 -0.336 0.769 0.132 0.184
## over_1.5
## over_2.5 -0.164 -0.236 0.135 0.104
## over_3.5 -0.425 -0.642 0.379 0.287 -0.132
## under_1.5 -0.119 0.329 -0.113 -0.232 -0.751 0.249 -0.157 -0.199
## under_2.5 0.114 -0.251
## under_3.5 -0.109
## Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16
## 1_NA 0.185 0.251
## 12_NA 0.171 -0.337 0.914
## 1X_NA -0.580 -0.692 -0.272
## 2_NA
## NO_NA 0.286 0.417 -0.118
## X2_NA 0.121 0.207
## YES_NA -0.504 -0.566 -0.116 0.104
## odd1_NA
## odd2_NA
## oddX_NA
## over_1.5 0.273 -0.952
## over_2.5 0.287 -0.326 -0.585 0.551 -0.162 0.140
## over_3.5 0.226 0.236 -0.197
## under_1.5 -0.310
## under_2.5 0.665 -0.515 0.287 -0.244 0.157 -0.183
## under_3.5 0.119 0.142 -0.121 0.931 0.252# Get principal component vectors using prcomp instead of princomp
pc1x2 = prcomp(dat1x2,center = TRUE,scale = TRUE)
# First 7 principal components
comp1x2 <- data.frame(pc1x2$x[,1:7])
# Plot
plot(comp1x2, pch=16, col=a1x2, main="Graph of Different PCs in 2-D")
ind1x2 <- get_pca_ind(pc1x2)
f1x2<-ind1x2$coord
##eigenvalues
eig.val1x2 <- get_eigenvalue(pc1x2)
eig.val1x2## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 5.81520173 36.34501083 36.34501
## Dim.2 4.26233605 26.63960033 62.98461
## Dim.3 3.38070808 21.12942550 84.11404
## Dim.4 1.21447177 7.59044858 91.70449
## Dim.5 0.37108323 2.31927021 94.02376
## Dim.6 0.32281186 2.01757413 96.04133
## Dim.7 0.22805859 1.42536620 97.46670
## Dim.8 0.13588317 0.84926984 98.31597
## Dim.9 0.07785377 0.48658606 98.80255
## Dim.10 0.05470026 0.34187664 99.14443
## Dim.11 0.03795848 0.23724050 99.38167
## Dim.12 0.02725929 0.17037057 99.55204
## Dim.13 0.02272841 0.14205258 99.69409
## Dim.14 0.02086661 0.13041631 99.82451
## Dim.15 0.01632796 0.10204978 99.92656
## Dim.16 0.01175071 0.07344194 100.00000fviz_eig(pc1x2)
##graph of indiviudals
fviz_pca_ind(pc1x2,
#col.ind = "cos2", # Color by the quality of representation
col.ind = a1x2, # Color by the quality of representation
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07")
#repel = TRUE # Avoid text overlapping
)
##graph of variables
fviz_pca_var(pc1x2,
col.var = "contrib", # Color by contributions to the PC
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
)
##graph combined
fviz_pca_biplot(pc1x2, #repel = TRUE,
col.var = "#2E9FDF", # Variables color
col.ind = a1x2
# col.ind = "#696969" # Individuals color
)
###Task 3
rawimage<-readJPEG('C:\\Users\\10025\\Desktop\\IE582\\hw2/hw2_image1.jpeg')
str(rawimage)## num [1:512, 1:512, 1:3] 0.122 0.141 0.141 0.192 0.114 ...plot(c(0, 512), c(0, 512), type = "n", xlab = "pixels", ylab = "pixels")
rasterImage(rawimage, 0, 0, 512, 512,
angle = 0, interpolate = TRUE)
red<-rawimage[,,1]
green<-rawimage[,,2]
blue<-rawimage[,,3]
par(mfrow=c(1,3))
image(t(red[nrow(red):1L,]),main="RED")
image(t(green[nrow(green):1L,]),main="GREEN")
image(t(blue[nrow(blue):1L,]),main="BLUE")
noise_1<-matrix(runif(512*512,min = 0,max = 0.1),512,512)
noise_2<-matrix(runif(512*512,min = 0,max = 0.1),512,512)
noise_3<-matrix(runif(512*512,min = 0,max = 0.1),512,512)
noised_image<-array(0,c(512,512,3))
noised_image[,,1]<-red_noise<-red+noise_1
noised_image[,,2]<-green_noise<-green+noise_2
noised_image[,,3]<-blue_noise<-blue+noise_3
noised_image[,,1]<-ifelse(noised_image[,,1]>1,1,noised_image[,,1])
noised_image[,,2]<-ifelse(noised_image[,,2]>1,1,noised_image[,,2])
noised_image[,,3]<-ifelse(noised_image[,,3]>1,1,noised_image[,,3])
par(mfrow=c(1,2))
plot(c(0, 512), c(0, 512), type = "n",main="original image", xlab = "", ylab = "")
rasterImage(rawimage, 0, 0, 512, 512,
angle = 0, interpolate = TRUE)
plot(c(0, 512), c(0, 512), type = "n",main="noised image", xlab = "", ylab = "")
rasterImage(noised_image, 0, 0, 512, 512,
angle = 0, interpolate = TRUE)
gray<-noised_image[,,1]+noised_image[,,2]+noised_image[,,3]
gray<-gray/max(gray)
par(mfrow=c(1,1))
plot(c(0, 512), c(0, 512), type = "n",main="grayscale image", xlab = "", ylab = "")
rasterImage(gray, 0, 0, 512, 512,
angle = 0, interpolate = TRUE)
noised_image<-array(0,c(512,512,3))
matrix<-matrix(0,260100,9)
for (i in 2:511) {
for(j in 2:511) {
matrix[510*(i-2)+j-1,1]<-gray[i-1,j-1]
matrix[510*(i-2)+j-1,2]<-gray[i-1,j]
matrix[510*(i-2)+j-1,3]<-gray[i-1,j+1]
matrix[510*(i-2)+j-1,4]<-gray[i,j-1]
matrix[510*(i-2)+j-1,5]<-gray[i,j]
matrix[510*(i-2)+j-1,6]<-gray[i,j+1]
matrix[510*(i-2)+j-1,7]<-gray[i+1,j-1]
matrix[510*(i-2)+j-1,8]<-gray[i+1,j]
matrix[510*(i-2)+j-1,9]<-gray[i+1,j+1]
}
}
dat<-matrix
colnames(dat) <- c("Upper left","upper","upper right","middle left","central","middle right","lower left","lower","lower right")
pc <- princomp(dat)
plot(pc)
summary(pc, loadings=T)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 0.6529131 0.06840902 0.049278038 0.038235138
## Proportion of Variance 0.9694645 0.01064260 0.005522401 0.003324654
## Cumulative Proportion 0.9694645 0.98010708 0.985629478 0.988954132
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 0.033436664 0.03139831 0.030713139 0.030091081
## Proportion of Variance 0.002542536 0.00224199 0.002145209 0.002059192
## Cumulative Proportion 0.991496668 0.99373866 0.995883866 0.997943058
## Comp.9
## Standard deviation 0.030074642
## Proportion of Variance 0.002056942
## Cumulative Proportion 1.000000000
##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
## Upper left 0.332 0.394 0.407 0.170 0.544 0.295 0.225
## upper 0.334 0.426 -0.447 -0.564 -0.238 0.358
## upper right 0.332 -0.410 0.391 0.302 -0.445 0.309 0.258 0.213
## middle left 0.333 0.420 0.231 -0.469 -0.282
## central 0.335 -0.502 -0.100 0.455 -0.644
## middle right 0.333 -0.420 0.230 -0.474 -0.387
## lower left 0.332 0.410 -0.390 0.303 -0.443 -0.310 0.256 0.160
## lower 0.334 -0.426 -0.448 0.563 -0.238 0.358
## lower right 0.333 -0.395 -0.407 0.171 0.545 -0.292 0.227 0.142
## Comp.9
## Upper left 0.314
## upper
## upper right -0.270
## middle left -0.599
## central
## middle right 0.534
## lower left 0.307
## lower
## lower right -0.292# Get principal component vectors using prcomp instead of princomp
pc = prcomp(dat,center = TRUE,scale = TRUE)
# First 9 principal components
comp <- data.frame(pc$x[,1:9])
#Results of PCAind <- get_pca_ind(pc)
# Eigenvalues
eig.val <- get_eigenvalue(pc)
eig.val## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 8.72517938 96.9464375 96.94644
## Dim.2 0.09578397 1.0642663 98.01070
## Dim.3 0.04970231 0.5522479 98.56295
## Dim.4 0.02992167 0.3324630 98.89541
## Dim.5 0.02288327 0.2542586 99.14967
## Dim.6 0.02017809 0.2242010 99.37387
## Dim.7 0.01930660 0.2145178 99.58839
## Dim.8 0.01853219 0.2059132 99.79431
## Dim.9 0.01851251 0.2056946 100.00000fviz_eig(pc)
##graph of variables
fviz_pca_var(pc,
col.var = "contrib", # Color by contributions to the PC
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
)
# Results for Variables
res.var <- get_pca_var(pc)
# Results for individuals
res.ind <- get_pca_ind(pc)
# Contribution to the first dimension
fviz_contrib(pc,choice = ("var"),axes = 1)
# Contribution to the second dimension
fviz_contrib(pc,choice = ("var"),axes = 2)
soul_image<-pc$x[,1]
new<-matrix(0,510,510)
for(k in 1:510){
for(l in 1:510){
new[k,l]<-soul_image[510*(k-1)+l]
}
} new_image<-normalizeData(new,type="0_1")
plot(c(0, 510), c(0, 510),main="PC1 Image", type = "n", xlab = "", ylab = "")
rasterImage(new_image, 0, 0, 510, 510,
angle = 0, interpolate = TRUE)
soul_image2<-pc$x[,2]
new2<-matrix(0,510,510)
for(k in 1:510){
for(l in 1:510){
new2[k,l]<-soul_image2[510*(k-1)+l]
}
}
new_image2<-normalizeData(new2,type="0_1")
plot(c(0, 510), c(0, 510),main="PC2 Image", type = "n", xlab = "", ylab = "")
rasterImage(new_image2, 0, 0, 510, 510,
angle = 0, interpolate = TRUE)
soul_image3<-pc$x[,3]
new3<-matrix(0,510,510)
for(k in 1:510){
for(l in 1:510){
new3[k,l]<-soul_image3[510*(k-1)+l]
}
}
new_image3<-normalizeData(new3,type="0_1")
plot(c(0, 510), c(0, 510),main="PC3 Image", type = "n", xlab = "", ylab = "")
rasterImage(new_image3, 0, 0, 510, 510,
angle = 0, interpolate = TRUE)
par(mfrow=c(1,3))
plot(c(0, 510), c(0, 510),main="PC1 Image", type = "n", xlab = "", ylab = "")
rasterImage(new_image, 0, 0, 510, 510,
angle = 0, interpolate = TRUE)
plot(c(0, 510), c(0, 510),main="PC2 Image", type = "n", xlab = "", ylab = "")
rasterImage(new_image2, 0, 0, 510, 510,
angle = 0, interpolate = TRUE)
plot(c(0, 510), c(0, 510),main="PC3 Image", type = "n", xlab = "", ylab = "")
rasterImage(new_image3, 0, 0, 510, 510,
angle = 0, interpolate = TRUE)